51问答网 > 计算①x눀-4／x눀-4x+3÷x눀+3x+2／x눀-x②2x+6／4-4x+x눀÷(x+3)·x눀+x-6／3-x

计算①x눀-4／x눀-4x+3÷x눀+3x+2／x눀-x②2x+6／4-4x+x눀÷(x+3)·x눀+x-6／3-x

2024-12-28 07:42:52

推荐回答（2个）

回答1：

①x²-4/x²-4x+3÷x²+3x+2/x²-x
=(x²-4)/(x²-4x+3)÷(x²+3x+2)/(x²-x)
=(x-2)(x+2)/(x-1)(x-3)÷(x+1)(x+2)/x(x-1)
=x(x-2)(x+2)(x-1)/[(x-1)(x-3)(x+1)(x+2)]
=(x²-2x)/(x²-2x-3)
②2x+6/4-4x+x²÷(x+3)·x²+x-6/3-x
=2(x+3)/(2-x)²÷(x+3)*(x+3)(x-2)/(3-x)
=(2x+3)/(-x²+5x-6)

回答2：

①x²-4／x²-4x+3÷x²+3x+2／x²-x
=(x²-4)/(x²-4x+3)÷(x²+3x+2)/(x²-x)
=(x-2)(x+2)/(x-1)(x-3)÷(x+1)(x+2)/x(x-1)
=x(x-2)(x+2)(x-1)/[(x-1)(x-3)(x+1)(x+2)]
=(x²-2x)/(x²-2x-3)

②2x+6／4-4x+x²÷(x+3)·x²+x-6／3-x
=2(x+3)/(2-x)²÷(x+3)*(x+3)(x-2)/(3-x)
=(2x+3)/(-x²+5x-6)